Testing system for determining the mechanical ... - Springer Link

Materials and Structures, 1994, 27, 324-330

Testing system for determining the mechanical behaviour of early age concrete under restrained and free uniaxial shrinkage K. K O V L E R National Building Research Institute, Technion - Israel Institute of Technology, Technion City, Haifa 32000, Israel A modified uniaxial restrained shrinkage test was developed, characterized by complete automation and high accuracy of measurements. The system developed was such that tensile stresses remained constant throughout the cross-section, excluding any premature failure of specimen. This testing arrangement enables separation of creep strain from shrinkage by means of simultaneous testing of twin specimens, one under restrained shrinkage, and the other under free shrinkage. A variety of mechanical characteristics of the concrete (individual components of strain, shrinkage stresses, moduli of elasticity, creep coefficient and tensile strength) may be determined in one test. Results using this testing arrangement are presented for concrete cured in sealed conditions for I day and then exposed to drying at 30~176 RH.

1. I N T R O D U C T I O N Cracking due to restrained shrinkage in concrete components such as highway pavements, slabs cast on grade and floors for parking garages can be of critical concern. However, a standard method for conducting restrained shrinkage tests does not exist. Many researchers use so-called ring specimens. In such tests ring-shaped test pieces of concrete are cast between two rigid (usually steel) rings, with the inner ring (core) providing the restraint when the specimen is kept in a drying environment, and shrinks against the core. Tensile stresses are induced in the material and cracking may occur. Recently, attempts to calculate the level of such stresses have been undertaken [1, 2]. However, it is rather difficult to determine these stresses accurately since the calculations are based on the theory of elasticity whereas the concrete is inelastic, in particular early age concrete. The visco-elastic response of the material causes some stress relaxation. Alexandrovsky [3] estimated that creep may lower the shrinkage stress by a factor of 2. Doubly restrained plate specimens may be subjected to a drying environment as well, and the resulting cracking is recorded and characterized [4]. However, the results depend on specimen geometry, and this test is not used for shrinkage stress calculation. Uniaxial shrinkage tests seem to be independent of specimen geometry and the tensile stresses induced by the restrained shrinkage may be evaluated directly. Alexandrovsky [3] thoroughly investigated uniaxial restrained shrinkage of concrete. He tested 5 0 m m • 50 mm x 210 mm beams which were exposed to drying only from the ends. Kasai et al. [5, 6] described two devices for early tensile strength. At both enlarged ends the specimen plates were connected to the concrete by bolts. Tensile stresses in such systems could be transferred also through an epoxy 0025-5432/94 (~) RILEM

interface [7] or by gripping specimens with contoured ends in a rigid frame [8]. A uniaxial specimen floating on a mercury bath was used by Orr and Haigh [9]. The testing apparatus was originally designed to measure shrinkage stresses in a restraint cement or mortar specimen. It was also possible to impose a constant rate of strain, by turning a screw drive with a constant speed electric motor and a pulley system. Paill6re et al. [10] used a system with which a concrete specimen could be tested at early age. During casting of the specimen the mould was placed horizontally. The swallow-tailed specimen was tested in the vertical position. The lower end was fixed, while the upper end was free to move and was connected to air pressure test equipment. Changes in specimen length were measured with inductive gauges having an accuracy of _+ 1 p.m. By maintaining the gauge length constant, shrinkage stresses could be registered; by changing the length stress or strain controlled, stress-strain relationships and estimations of modulus of elasticity could be obtained. It has been argued [11] that one of the disadvantages of this test is the vertical positioning of the specimen, because the dead load of the specimen often causes rupture in the upper part. A modified system of the same nature, but with a horizontal arrangement was used for the study of high strength concrete [12]. In general, uniaxial restrained shrinkage tests seem to be independent of specimen g e o m e t r y and restraint conditions and may be used for the determination of stress-strain relationships and modulus of elasticity, in addition to restrained shrinkage stresses. However, under one-dimensional restraint the test is similar to a uniaxial tension test, and therefore prone to the errors and difficulties inherent in such a test. The present work was aimed at developing a modified uniaxial restrained shrinkage test for early age concrete,

Materials and Structures characterized by a fully automated closed loop control, as well as high accuracy of measurements, soft and regular loading. In addition, the testing system was designed to make it possible to resolve creep strain from shrinkage strain, and to determine a variety of mechanical characteristics of the concrete.

2. C L O S E D L O O P UNIAXIALLY RESTRAINED S H R I N K A G E T E S T I N G APPARATUS A general view of the experimental device is shown in Fig. I. There are two specimens of length 1.0 m mounted horizontally on the laboratory table, one for restrained, and the other for free shrinkage test. This system is a modification of a prototype developed by Bloom and Bentur [123. The right end of each specimen is fixed. The displacements of the left movable grips were measured by a linearly variable displacement transducer (LVDT). Each displacement measurement cycle consisted of 256 measurements during 0.5 s, and the result was averaged. Such a procedure permitted very high accuracy and reproducibility of linear displacement measurements - not worse than +_0.1 p.m. The stresses in the restrained specimen were measured

Fig. 1 Experimental device showing (top) a general view and (bottom) the movable grips, together with the loading and measurement devices.

325 by means of a load cell with an accuracy of +_0.3 kPa. The restrained specimen was loaded by a computercontrolled stepper motor according to a special program. The compensation cycle began when the absolute value of the total restrained specimen strain exceeded 5 x 10 -6 (5 p.m for the 1.0m specimen). Load was applied to recover the shrinkage strain. Two different rates of loading were chosen. In the initial period of fast evaporation and resultant drastic growth of shrinkage strain (period A), the loading rate was accepted to be 3 kPa s -1, and in the following stable stage (period B) 1 kPa s- 1. The frequency of stress and strain measurements in these stages of the shrinkage process was chosen differently as well. Usually, the time interval between measurements in period A was taken as 3 rain, and in period B it was 10 min. The duration of period A was usually accepted as 1-2 h. Loading rates associated with shrinkage rates were chosen to exclude premature specimen failure. For the same purpose the grips were of a special shape, characterized by gradual widening of the internal part to eliminate any stress concentrations inside (Fig. 2). The possible physical eccentricity of the specimen, caused by non-uniform strain development in the net cross-section, was checked and excluded. The movable grips were joined with spherical hinges. During the test the uniformity of progressive displacements of the grip was controlled on the left and right grip sides by means of two mechanical ~train gauges of accuracy _+ 1 pm: when the difference in their readings was more than 5 gm, the centre of the hinge was moved horizontally (by means of precise screws) to the necessary direction. The measured value of the friction force did not exceed 20 N, and was therefore neglected at data analysis. At the end of the testing period the specimens were unloaded and then loaded to failure at a rate of 3 kPa s- 1, with simultaneous measurement of deformation. This served to determine the sti'ess-strain curve of the concrete.

Fig. 2 The shape of the specimen grip.

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3. UNIAXIAL RESTRAINED AND FREE S H R I N K A G E TEST AS A M E T H O D FOR DETERMINING THE MAIN MECHANICAL CHARACTERISTICS O F C O N C R E T E

3.1 Analytical considerations It is known that at any time t during a fully restrained shrinkage test the total concrete strain ~ is to be zero. However, the individual elastic (e~), creep (Ec) and shrinkage (Esh) components of concrete strain have finite values: E(t) = Ee(t ) + Ec(t ) + Esh(t) : 0 (1) The elastic strain may be expressed as

o-(t) E(t)

Ee(t) -

(2)

where E(t) is the elastic (secant) modulus of concrete, dependent on time in the general case. The creep strain due to a constant stress a is o

Ec(t) = E-~ q~(t)

(3)

where q~(t) is the creep coefficient, defined as the ratio between the creep and elastic strains. If the elastic and creep components of strain are combined, a reduced (effective) modulus for concrete Eeff(t) can be defined as follows:

E(t) = ~

o"

[1 + 4,(t)] + Esh(t)

G

--

+ Esh (t)

(4)

Eeff(t)

where

g(t) 1 + ~(0

Eefe(t ) - - -

(5)

However, stresses in a restrained shrinking element correspond to stresses induced in it by a gradually increasing load. It is known that the creep of concrete under a gradually increasing load progresses more slowly than under the constant stress a which is applied from the beginning of the test [13]. That is why instead of the creep coefficient q~(t) one should use the reduced creep coefficient O(t)~b(t), where Q(t) is often called the ageing coefficient, and its magnitude generally falls within the range 0.6-0.9 for ordinary hardened concrete and 0.9-1.0 for young concrete [14]. Because the concrete stress is applied gradually, the sum of the elastic and creep strains is related to the stress by the age-adjusted effective modulus, developed by Ba2ant [13]:

E'eff(t) -

E(t) 1 + .Q(t)c/)(t)

(6)

Equation 4 may be rewritten as

a(t) E'~ff(t)

-- -- 6sh(t)

(7)

Fig. 3 Creep strain calculated from the data of restrained and free shrinkage tests. Another relation that is of significance here is the one which characterizes the compensation cycle at the stage where incremental load is applied to keep the specimen at zero strain (elastic strain in Fig. 3). Here, the incremental stress and elastic strain follow this relation: de(t ) --

,~(t) Et(t)

(8)

where Et(t ) is the tangential modulus at the specific load level. If we have the results of stress and elastic strain measurements in a uniaxial restrained shrinkage test and the shrinkage strain measurements in a uniaxial free shrinkage test held simultaneously on the twin specimens, it is possible to determine all three moduli of elasticity: secant, age-adjusted effective and tangential, according to Equations 2, 7 and 8, respectively. As far as the creep coefficient ~2(t)c~(t) is concerned, its values may be obtained just from deformation data on restrained and free shrinkage twin specimens, without any information about stress. Let us consider Fig. 3, which shows the method of creep strain calculation from a uniaxial shrinkage test carried out on restrained and free companion specimens. The restrained shrinkage test is based on so-called 'compensation cycles'. The total strain of the.restrained specimen ~(t) during the whole test must be zero according to Equation 1. If the absolute value of E(t) exceeds some small border value, the motor begins to return it to zero. In the present study, the border value was a strain of + 5 x 10 -6, i.e., deformation of 5 ~tm in the 1.0 m long specimen. Each compensation cycle shown in Fig. 3 consists of shrinkage + creep strain compensated by instantaneous elastic strain, which is induced by means of an incremental load applied by the computercontrolled motor. Due to these compensation cycles the sum of elastic strains at any time t is equal to that of the shrinkage + creep strains by absolute value. That is why if the stiffness of the experimental device is neglected the sum of the shrinkage and creep strains to the given time tk may be

Materials and Structures

327

calculated as half of the negative sum of the absolute values of all the preceding increments of deformation measured on the restrained specimen: E~h(t~) + Ec(r~) : --~

[I-E(ti)-- E(tl- X)]I

(9)

i=l

E(ti) is the strain measured at time ti, intermediate between 0 and t k, with the previous measurement being at time t ~ - 1. This curve is shown in Fig. 3 as the 'shrinkage + creep cumulative curve'. So the creep strain may be calculated as the difference between the free shrinkage curve and the shrinkage + creep cumulative curve, and the creep coefficient is determined as o ( t ) ~ ( t ) - Eo(tj _ Esh(t) Eo(t) Esh(t) + ~o(t)

1

(10)

A similar method of creep function determination was applied by Penev and Kawamura [15] for soil-cement mixtures. It is necessary to emphasize that the definition of the creep coefficient as given in Equation 10 is different from the common one, which is usually the ratio between the creep strain determined at a fixed age and the elastic strain. In the present paper the elastic strain is not a constant value, but corresponds to the strain at the time considered.

3.2 Requirement for the experimental equipment It is important to develop a high accuracy method for displacement measurement for this kind of test because the absolute values of the deformations will be close to zero. It means that the total deformation of the specimen, equalling the sum of shrinkage and creep components, should be compensated for by instantaneous deformation quite frequently during the test, in order to provide more gradual growth of tensile stress. If this condition is not met, large and sudden irregular compensations of deformation will be needed, and they may cause premature specimen failure. This will occur more readily when the tensile strength of the material is not much more than the value of the tensile stress induced in it at a given time. The physical eccentricity in the specimen caused by non-uniformity in deformation distribution over the cross-section, or by stress concentration in the grips, can also lead to premature failure. As is well known, all tensile test schemes are very sensitive to these factors. It would be expedient, after basic shrinkage tests, to check the tensile strength of the material and to determine by how much it is greater than the level of the tensile stress induced by the restrained shrinking. Thus, by means of a uniaxial restrained shrinkage test, simultaneously with a free shrinking companion specimen, it is quite possible to obtain a variety of mechanical characteristics of early age concrete, concerning its behaviour under uniaxial tension, namely:

(a) individual elastic creep and shrinkage components of concrete strain; (b) creep coefficient under gradually increasing tensile load; (c) elasticity moduli (secant, age-adjusted effective and tangential); (d) tensile stress due to restrained shrinkage; (e) tensile strength of the concrete at the end of the shrinkage period. The experimental techniques provided for this test should have the following features: (i) high accuracy of linear displacement measurement; (ii) complete automation of the experiment, both in data registration and in governing the specimen loading; (iii) exclusion of any premature specimen failure, which may be the result of irregular or large loading steps, or due to possible physical eccentricity of the specimen and stress concentration in the grips. The apparatus described in Section 2 was designed to meet these requirements. 4. BEHAVIOUR O F EARLY AGE C O N C R E T E The investigation was aimed at studying the mechanical behaviour of young concrete exposed to uniaxial restrained and free shrinkage in hot climate, to demonstrate the usefulness of the, testing system described here. The time dependence of the following mechanical characteristics was investigated: stresses, deformations, elasticity moduli, tensile strengths and creep coefficients. The concrete investigated is defined as microconcrete, with maximum aggregate size of 7 mm, specially graded for this purpose. 4.1 Experimental details The materials used in this study were: ordinary Portland cement having a standard compressive strength of 30 MPa and a specific gravity of 3.1 g cm-3; coarse aggregate - crushed dolomite gravel with a maximum particle size or 7 mm and a specific gravity of 2.75 g c m - 3; and fine aggregate - quartz sand from a natural source having a fineness modulus of 1.76 and a specific gravity of 2.63 g c m - 3. The concrete composition (cement: sand: gravel by weight) was 1:2:2 at a water/cement ratio w/c = 0.5. Shrinkage tests were carried out in special horizontal beam moulds with net cross-section of 40 mm • 40 mm. There were twin specimens, one for restrained, and the other for free shrinkage, each with a working length of 1000 mm and special grips were used as described in Section 2. A third specimen of 500 mm working length without any load grips was cast and mounted on an automatic digital balance having an accuracy of _+0.1 g, for simultaneous measurement of weight loss and free shrinkage deformation. The specimens were cast and exposed to drying in a

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Kovler

special environmental room having a temperature of 30 _+ I~ and air relative humidity of 40 + 3%, which simulated hot climate conditions. Immediately after casting, the upper surface of each specimen was reliably protected against any water evaporation by means of a synthetic film tightly applied onto the fresh concrete surface with no visible trapped air. The specimens were demoulded after 1 day, and then exposed to a drying environment for a period of 1 day. During the first day they were not restrained. At the end of the shrinkage test, both restrained and free specimens were tested in the same device under uniaxial short-term tension in order to obtain a stressstrain diagram and the tensile strength of the material. The restrained specimens were unloaded before, and thus the hysteresis of the unloading and loading cycle was also obtained.

4.2 Results and discussion

4.2.1 Deformations and stresses The results of strain and stress measurements are presented in Fig. 4. Time zero represents the initiation of drying, i.e., one day old concrete, cured before that under sealed conditions. The absolute value of free shrinkage strain, E~h(t) reached (120-180) x 10 -6 after 1 day and (220-280) x 10 -6 after 2 days of drying. These values are the ranges obtained in the testing of 6 specimens. The tensile stresses develop rather intensively under restraint conditions and reach 1.5-1.6 MPa after 1 day and 2.1-2.3 MPa after 2 days of drying. Particular attention should be given to the drastic growth in the restraining stresses immediately after exposure (the steep slope in the stress curve in Fig. 4). This can involve risks on site, because there are no opportunities to control and govern the uniformity of the stress-strain state as in the laboratory, which can result in localization of tensile deformations and lead to cracking of the restrained element.

Special influences should be noted at the first stage of drying. Initially there is a hygral shock for a period of 15-25 minutes, after which the deformation is stabilized and even some swelling occurs. This peculiar behaviour is probably associated with the strain gradient in the cross-section, and perhaps with some thermal effect as the specimen is being cooled slightly during drying. 4.2.2 Creep coefficient In Fig. 4, the curve of the creep deformation Ec(t) is shown. The creep coefficient values are given in Fig. 5, calculated according to Equation 10. The values of the creep coefficient for well cured hardened concrete are small (0.3-0.5), and they tend to increase with time. 4.2.3 Elasticity moduli The values of secant and age-adjusted effective elasticity moduli calculated according to Equations 2 and 7 are presented in Fig. 5, providing typical examples for early age concrete under restrained conditions. Fig. 5 includes also calculated values of the tangential elasticity modulus, which is defined as the ratio between the stress and strain increments measured in one hour, according to Equation 8. The values of both secant and age-adjusted effective moduli are quite close to each other (due to the small value of the creep coefficient) and remain practically unchanged during at least the first day of drying (Fig. 5). The fact that the tangential modulus in Fig. 5 varies over a range in a somewhat cyclic manner may be associated with the fact that at different times the incremental load is applied at a stage where the ratio between the existing stress and strength is not the same. Another parameter of influence is obviously the overall change of the elastic response with time. 4.2.4 Stress-strain diagrams Some relations between stress and elastic strain derived at the various stages of the experiment are shown in

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Fig. 5 Elasticity moduli and creep coefficientversus drying time.

M a t e r i a l s and S t r u c t u r e s

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